As a presidential candidate in August 2015, Donald Trump huddled with a longtime friend, media executive David Pecker, in his cluttered 26th floor Trump Tower office and made a request.

Mr. Pecker, chief executive of American Media Inc., offered to use his National Enquirer tabloid to buy the silence of women if they tried to publicize alleged sexual encounters with Mr. Trump.

The Trump Tower meeting and its aftermath are among several previously unreported instances in which Mr. Trump intervened directly to suppress stories about his alleged sexual encounters with women, according to interviews with three dozen people who have direct knowledge of the events or who have been briefed on them, as well as court papers, corporate records and other documents.

The Wall Street Journal found that Mr. Trump was involved in or briefed on nearly every step of the agreements.